// Extend the Array class
Array.prototype.max = function() {
  return Math.max.apply(null, this);
};
Array.prototype.min = function() {
  return Math.min.apply(null, this);
};
Array.prototype.mean = function() {
  var i, sum;
  for(i=0,sum=0;i<this.length;i++)
    sum += this[i];
  return sum / this.length;
};
Array.prototype.rep = function(n) {
  return Array.apply(null, new Array(n))
    .map(Number.prototype.valueOf, this[0]);
};
Array.prototype.pip = function(x, y) {
  var i, j, c = false;
  for(i=0,j=this.length-1;i<this.length;j=i++) {
    if( ((this[i][1]>y) != (this[j][1]>y)) &&
      (x<(this[j][0]-this[i][0]) * (y-this[i][1]) / (this[j][1]-this[i][1]) + this[i][0]) ) {
      c = !c;
    }
  }
  return c;
}

var kriging = function() {
  var kriging = {};

  // Matrix algebra
  kriging_matrix_diag = function(c, n) {
    var i, Z = [0].rep(n*n);
    for(i=0;i<n;i++) Z[i*n+i] = c;
    return Z;
  };
  kriging_matrix_transpose = function(X, n, m) {
    var i, j, Z = Array(m*n);
    for(i=0;i<n;i++)
      for(j=0;j<m;j++)
        Z[j*n+i] = X[i*m+j];
    return Z;
  };
  kriging_matrix_scale = function(X, c, n, m) {
    var i, j;
    for(i=0;i<n;i++)
      for(j=0;j<m;j++)
        X[i*m+j] *= c;
  };
  kriging_matrix_add = function(X, Y, n, m) {
    var i, j, Z = Array(n*m);
    for(i=0;i<n;i++)
      for(j=0;j<m;j++)
        Z[i*m+j] = X[i*m+j] + Y[i*m+j];
    return Z;
  };
  // Naive matrix multiplication
  kriging_matrix_multiply = function(X, Y, n, m, p) {
    var i, j, k, Z = Array(n*p);
    for(i=0;i<n;i++) {
      for(j=0;j<p;j++) {
        Z[i*p+j] = 0;
        for(k=0;k<m;k++)
          Z[i*p+j] += X[i*m+k]*Y[k*p+j];
      }
    }
    return Z;
  };
  // Cholesky decomposition
  kriging_matrix_chol = function(X, n) {
    var i, j, k, sum, p = Array(n);
    for(i=0;i<n;i++) p[i] = X[i*n+i];
    for(i=0;i<n;i++) {
      for(j=0;j<i;j++)
        p[i] -= X[i*n+j]*X[i*n+j];
      if(p[i]<=0) return false;
      p[i] = Math.sqrt(p[i]);
      for(j=i+1;j<n;j++) {
        for(k=0;k<i;k++)
          X[j*n+i] -= X[j*n+k]*X[i*n+k];
        X[j*n+i] /= p[i];
      }
    }
    for(i=0;i<n;i++) X[i*n+i] = p[i];
    return true;
  };
  // Inversion of cholesky decomposition
  kriging_matrix_chol2inv = function(X, n) {
    var i, j, k, sum;
    for(i=0;i<n;i++) {
      X[i*n+i] = 1/X[i*n+i];
      for(j=i+1;j<n;j++) {
        sum = 0;
        for(k=i;k<j;k++)
          sum -= X[j*n+k]*X[k*n+i];
        X[j*n+i] = sum/X[j*n+j];
      }
    }
    for(i=0;i<n;i++)
      for(j=i+1;j<n;j++)
        X[i*n+j] = 0;
    for(i=0;i<n;i++) {
      X[i*n+i] *= X[i*n+i];
      for(k=i+1;k<n;k++)
        X[i*n+i] += X[k*n+i]*X[k*n+i];
      for(j=i+1;j<n;j++)
        for(k=j;k<n;k++)
          X[i*n+j] += X[k*n+i]*X[k*n+j];
    }
    for(i=0;i<n;i++)
      for(j=0;j<i;j++)
        X[i*n+j] = X[j*n+i];

  };
  // Inversion via gauss-jordan elimination
  kriging_matrix_solve = function(X, n) {
    var m = n;
    var b = Array(n*n);
    var indxc = Array(n);
    var indxr = Array(n);
    var ipiv = Array(n);
    var i, icol, irow, j, k, l, ll;
    var big, dum, pivinv, temp;

    for(i=0;i<n;i++)
      for(j=0;j<n;j++) {
        if(i==j) b[i*n+j] = 1;
        else b[i*n+j] = 0;
      }
    for(j=0;j<n;j++) ipiv[j] = 0;
    for(i=0;i<n;i++) {
      big = 0;
      for(j=0;j<n;j++) {
        if(ipiv[j]!=1) {
          for(k=0;k<n;k++) {
            if(ipiv[k]==0) {
              if(Math.abs(X[j*n+k])>=big) {
                big = Math.abs(X[j*n+k]);
                irow = j;
                icol = k;
              }
            }
          }
        }
      }
      ++(ipiv[icol]);

      if(irow!=icol) {
        for(l=0;l<n;l++) {
          temp = X[irow*n+l];
          X[irow*n+l] = X[icol*n+l];
          X[icol*n+l] = temp;
        }
        for(l=0;l<m;l++) {
          temp = b[irow*n+l];
          b[irow*n+l] = b[icol*n+l];
          b[icol*n+l] = temp;
        }
      }
      indxr[i] = irow;
      indxc[i] = icol;

      if(X[icol*n+icol]==0) return false; // Singular

      pivinv = 1 / X[icol*n+icol];
      X[icol*n+icol] = 1;
      for(l=0;l<n;l++) X[icol*n+l] *= pivinv;
      for(l=0;l<m;l++) b[icol*n+l] *= pivinv;

      for(ll=0;ll<n;ll++) {
        if(ll!=icol) {
          dum = X[ll*n+icol];
          X[ll*n+icol] = 0;
          for(l=0;l<n;l++) X[ll*n+l] -= X[icol*n+l]*dum;
          for(l=0;l<m;l++) b[ll*n+l] -= b[icol*n+l]*dum;
        }
      }
    }
    for(l=(n-1);l>=0;l--)
      if(indxr[l]!=indxc[l]) {
        for(k=0;k<n;k++) {
          temp = X[k*n+indxr[l]];
          X[k*n+indxr[l]] = X[k*n+indxc[l]];
          X[k*n+indxc[l]] = temp;
        }
      }

    return true;
  }

  // Variogram models
  kriging_variogram_gaussian = function(h, nugget, range, sill, A) {
    return nugget + ((sill-nugget)/range)*
      ( 1.0 - Math.exp(-(1.0/A)*Math.pow(h/range, 2)) );
  };
  kriging_variogram_exponential = function(h, nugget, range, sill, A) {
    return nugget + ((sill-nugget)/range)*
      ( 1.0 - Math.exp(-(1.0/A) * (h/range)) );
  };
  kriging_variogram_spherical = function(h, nugget, range, sill, A) {
    if(h>range) return nugget + (sill-nugget)/range;
    return nugget + ((sill-nugget)/range)*
      ( 1.5*(h/range) - 0.5*Math.pow(h/range, 3) );
  };

  // Train using gaussian processes with bayesian priors
  kriging.train = function(t, x, y, model, sigma2, alpha) {
    var variogram = {
      t      : t,
      x      : x,
      y      : y,
      nugget : 0.0,
      range  : 0.0,
      sill   : 0.0,
      A      : 1/3,
      n      : 0
    };
    switch(model) {
      case "gaussian":
        variogram.model = kriging_variogram_gaussian;
        break;
      case "exponential":
        variogram.model = kriging_variogram_exponential;
        break;
      case "spherical":
        variogram.model = kriging_variogram_spherical;
        break;
    };

    // Lag distance/semivariance
    var i, j, k, l, n = t.length;
    var distance = Array((n*n-n)/2);
    for(i=0,k=0;i<n;i++)
      for(j=0;j<i;j++,k++) {
        distance[k] = Array(2);
        distance[k][0] = Math.pow(
          Math.pow(x[i]-x[j], 2)+
          Math.pow(y[i]-y[j], 2), 0.5);
        distance[k][1] = Math.abs(t[i]-t[j]);
      }
    distance.sort(function(a, b) { return a[0] - b[0]; });
    variogram.range = distance[(n*n-n)/2-1][0];

    // Bin lag distance
    var lags = ((n*n-n)/2)>30?30:(n*n-n)/2;
    var tolerance = variogram.range/lags;
    var lag = [0].rep(lags);
    var semi = [0].rep(lags);
    if(lags<30) {
      for(l=0;l<lags;l++) {
        lag[l] = distance[l][0];
        semi[l] = distance[l][1];
      }
    }
    else {
      for(i=0,j=0,k=0,l=0;i<lags&&j<((n*n-n)/2);i++,k=0) {
        while( distance[j][0]<=((i+1)*tolerance) ) {
          lag[l] += distance[j][0];
          semi[l] += distance[j][1];
          j++;k++;
          if(j>=((n*n-n)/2)) break;
        }
        if(k>0) {
          lag[l] /= k;
          semi[l] /= k;
          l++;
        }
      }
      if(l<2) return variogram; // Error: Not enough points
    }

    // Feature transformation
    n = l;
    variogram.range = lag[n-1]-lag[0];
    var X = [1].rep(2*n);
    var Y = Array(n);
    var A = variogram.A;
    for(i=0;i<n;i++) {
      switch(model) {
        case "gaussian":
          X[i*2+1] = 1.0-Math.exp(-(1.0/A)*Math.pow(lag[i]/variogram.range, 2));
          break;
        case "exponential":
          X[i*2+1] = 1.0-Math.exp(-(1.0/A)*lag[i]/variogram.range);
          break;
        case "spherical":
          X[i*2+1] = 1.5*(lag[i]/variogram.range)-
            0.5*Math.pow(lag[i]/variogram.range, 3);
          break;
      };
      Y[i] = semi[i];
    }

    // Least squares
    var Xt = kriging_matrix_transpose(X, n, 2);
    var Z = kriging_matrix_multiply(Xt, X, 2, n, 2);
    Z = kriging_matrix_add(Z, kriging_matrix_diag(1/alpha, 2), 2, 2);
    var cloneZ = Z.slice(0);
    if(kriging_matrix_chol(Z, 2))
      kriging_matrix_chol2inv(Z, 2);
    else {
      kriging_matrix_solve(cloneZ, 2);
      Z = cloneZ;
    }
    var W = kriging_matrix_multiply(kriging_matrix_multiply(Z, Xt, 2, 2, n), Y, 2, n, 1);

    // Variogram parameters
    variogram.nugget = W[0];
    variogram.sill = W[1]*variogram.range+variogram.nugget;
    variogram.n = x.length;

    // Gram matrix with prior
    n = x.length;
    var K = Array(n*n);
    for(i=0;i<n;i++) {
      for(j=0;j<i;j++) {
        K[i*n+j] = variogram.model(Math.pow(Math.pow(x[i]-x[j], 2)+
          Math.pow(y[i]-y[j], 2), 0.5),
          variogram.nugget,
          variogram.range,
          variogram.sill,
          variogram.A);
        K[j*n+i] = K[i*n+j];
      }
      K[i*n+i] = variogram.model(0, variogram.nugget,
        variogram.range,
        variogram.sill,
        variogram.A);
    }

    // Inverse penalized Gram matrix projected to target vector
    var C = kriging_matrix_add(K, kriging_matrix_diag(sigma2, n), n, n);
    var cloneC = C.slice(0);
    if(kriging_matrix_chol(C, n))
      kriging_matrix_chol2inv(C, n);
    else {
      kriging_matrix_solve(cloneC, n);
      C = cloneC;
    }

    // Copy unprojected inverted matrix as K
    var K = C.slice(0);
    var M = kriging_matrix_multiply(C, t, n, n, 1);
    variogram.K = K;
    variogram.M = M;

    return variogram;
  };

  // Model prediction
  kriging.predict = function(x, y, variogram) {
    var i, k = Array(variogram.n);
    for(i=0;i<variogram.n;i++)
      k[i] = variogram.model(Math.pow(Math.pow(x-variogram.x[i], 2)+
        Math.pow(y-variogram.y[i], 2), 0.5),
        variogram.nugget, variogram.range,
        variogram.sill, variogram.A);
    return kriging_matrix_multiply(k, variogram.M, 1, variogram.n, 1)[0];
  };
  kriging.variance = function(x, y, variogram) {
    var i, k = Array(variogram.n);
    for(i=0;i<variogram.n;i++)
      k[i] = variogram.model(Math.pow(Math.pow(x-variogram.x[i], 2)+
        Math.pow(y-variogram.y[i], 2), 0.5),
        variogram.nugget, variogram.range,
        variogram.sill, variogram.A);
    return variogram.model(0, variogram.nugget, variogram.range,
      variogram.sill, variogram.A)+
      kriging_matrix_multiply(kriging_matrix_multiply(k, variogram.K,
        1, variogram.n, variogram.n),
        k, 1, variogram.n, 1)[0];
  };

  // Gridded matrices or contour paths
  kriging.grid = function(polygons, variogram, width) {
    var i, j, k, n = polygons.length;
    if(n==0) return;

    // Boundaries of polygons space
    var xlim = [polygons[0][0][0], polygons[0][0][0]];
    var ylim = [polygons[0][0][1], polygons[0][0][1]];
    for(i=0;i<n;i++) // Polygons
      for(j=0;j<polygons[i].length;j++) { // Vertices
        if(polygons[i][j][0]<xlim[0])
          xlim[0] = polygons[i][j][0];
        if(polygons[i][j][0]>xlim[1])
          xlim[1] = polygons[i][j][0];
        if(polygons[i][j][1]<ylim[0])
          ylim[0] = polygons[i][j][1];
        if(polygons[i][j][1]>ylim[1])
          ylim[1] = polygons[i][j][1];
      }

    // Alloc for O(n^2) space
    var xtarget, ytarget;
    var a = Array(2), b = Array(2);
    var lxlim = Array(2); // Local dimensions
    var lylim = Array(2); // Local dimensions
    var x = Math.ceil((xlim[1]-xlim[0])/width);
    var y = Math.ceil((ylim[1]-ylim[0])/width);

    var A = Array(x+1);
    for(i=0;i<=x;i++) A[i] = Array(y+1);
    for(i=0;i<n;i++) {
      // Range for polygons[i]
      lxlim[0] = polygons[i][0][0];
      lxlim[1] = lxlim[0];
      lylim[0] = polygons[i][0][1];
      lylim[1] = lylim[0];
      for(j=1;j<polygons[i].length;j++) { // Vertices
        if(polygons[i][j][0]<lxlim[0])
          lxlim[0] = polygons[i][j][0];
        if(polygons[i][j][0]>lxlim[1])
          lxlim[1] = polygons[i][j][0];
        if(polygons[i][j][1]<lylim[0])
          lylim[0] = polygons[i][j][1];
        if(polygons[i][j][1]>lylim[1])
          lylim[1] = polygons[i][j][1];
      }

      // Loop through polygon subspace
      a[0] = Math.floor(((lxlim[0]-((lxlim[0]-xlim[0])%width)) - xlim[0])/width);
      a[1] = Math.ceil(((lxlim[1]-((lxlim[1]-xlim[1])%width)) - xlim[0])/width);
      b[0] = Math.floor(((lylim[0]-((lylim[0]-ylim[0])%width)) - ylim[0])/width);
      b[1] = Math.ceil(((lylim[1]-((lylim[1]-ylim[1])%width)) - ylim[0])/width);
      for(j=a[0];j<=a[1];j++)
        for(k=b[0];k<=b[1];k++) {
          xtarget = xlim[0] + j*width;
          ytarget = ylim[0] + k*width;
          if(polygons[i].pip(xtarget, ytarget))
            A[j][k] = kriging.predict(xtarget,
              ytarget,
              variogram);
        }
    }
    A.xlim = xlim;
    A.ylim = ylim;
    A.zlim = [variogram.t.min(), variogram.t.max()];
    A.width = width;
    return A;
  };
  kriging.contour = function(value, polygons, variogram) {

  };

  // Plotting on the DOM
  kriging.plot = function(canvas, grid, xlim, ylim, colors) {
    // Clear screen
    var ctx = canvas.getContext("2d");
    ctx.clearRect(0, 0, canvas.width, canvas.height);

    // Starting boundaries
    var range = [xlim[1]-xlim[0], ylim[1]-ylim[0], grid.zlim[1]-grid.zlim[0]];
    var i, j, x, y, z;
    var n = grid.length;
    var m = grid[0].length;
    var wx = Math.ceil(grid.width*canvas.width/(xlim[1]-xlim[0]));
    var wy = Math.ceil(grid.width*canvas.height/(ylim[1]-ylim[0]));
    for(i=0;i<n;i++)
      for(j=0;j<m;j++) {
        if(grid[i][j]==undefined) continue;
        x = canvas.width*(i*grid.width+grid.xlim[0]-xlim[0])/range[0];
        y = canvas.height*(1-(j*grid.width+grid.ylim[0]-ylim[0])/range[1]);
        z = (grid[i][j]-grid.zlim[0])/range[2];
        if(z<0.0) z = 0.0;
        if(z>1.0) z = 1.0;

        ctx.fillStyle = colors[Math.floor((colors.length-1)*z)];
        ctx.fillRect(Math.round(x-wx/2), Math.round(y-wy/2), wx, wy);
      }

  };


  return kriging;
}();